A really tough nut, Ruud. IMHO it was harder than your album killer. But after I realized what the key was it got easier. So here is the walkthrough, as always in tiny font.
Edit: Additions/corrections in blue, thanks to Ed
Walkthrough Assassin 38
0. Preliminary steps
0a. 26(4) at r1c1 : no 1
0b. 11(3) at r2c2 : no 9
0c. 8(3) at r1c3 : no 6,7,8,9
0d. 13(2) at r1c5 and r6c1 : no 1,2,3
0e. 27(4) at r3c6 : no 1,2
0f. 9(2) at r4c1 and r6c5 : no 9
0g. 6(2) at r4c8 : no 3,6,7,8,9
0h. 12(2) at r5c1 : no 1,2,6
0i. 7(2) at r5c6 : no 7,8,9
0j. 14(2) at r5c8 : no 1,2,3,4,7
0k. 10(2) at r6c8 and r8c5 : no 5
0l. 22(3) at r8c4 : no 1,2,3,4
1. 45 on N1 : r13c3 = 8(2) = [17|26]|{35}
2. 45 on N7 : r79c3 = 17(2) = {89] -> 8,9 locked for c3 and N7
3. 45 on N3 : r13c7 = 15(2) = {69|78}
4. 45 on N9 : r79c7 = 6(2) = {15|24}
5. 45 on c12 : r28c3 = 9(2) = {27|36|45}
6. 45 on c89 : r28c7 = 9(2) = {18|27|36} ({45} blocked by 6(29 from step 4)
7. 45 on N4 : r456c3 = 11(3) = {137|146|236|245}
8. 45 on N6 : r456c7 = 15(3) = {159|249|357} ({258|456} blocked by 14(2), {267|348} blocked by 6(2) and 14(2), {168} blocked by step 3) -> no 6,8 -> no1 in r5c6
9. 45 on r5 : r5c345 = 12(3) = {129|147|237} ({156} blocked by 14(2), {345} blocked by 12(2), {138} blocked by 12(2) and 14(2), {246} blocked by 7(2)) -> no 5,6,8
10. 45 on c5 : r345c5 = 13(3)
10a. 45 on c5 : r3c5 + 4 = r45c4 -> r3c5 : 1..9 , r45c4 : 5..13
11. r4 : 9(2) = {18|27|36} ({4,5} blocked by 6(2))
12. N12 : 8(3) = 1{25|34} -> 1 locked for 8(3) -> no 1 in r1c6
13. N78 : 22(3) = 9{58|67} -> 9 locked for 22(3) -> no 9 in r9c56 -> no 1 in r8c5
14. N6 : 10(2) = {19|37} ({28|46} blocked by 6(2) and 14(2))
15. N1 : 9 locked in 26(4) = 9{278|368|458|467}
16. N3 : 18(4) = {1269|1278|1359|1458|2349|2358|2457|3456} ({1368|1467|2367} blocked by 15(2) from step 3)
17. 20(4) at r6c3 : must have at least one of {89} -> {2567|3467} not possible
18. 45 on N8 : r7c456 = r9c37 = 9..14
19. 45 on N2 : r1c37 + 6 = r3c456 -> r1c37 : 7..14 , r3c456 : 13..20
20. 45 on N123 : r45c3 + 2 = r3c67
using step 7:
20a. min r3c67 : 9 -> min r45c3 : 7
20b. max r45c3 : 10 -> max r3c67 : 12
20c. -> r6c3 = {1234}, r3c6 = {345}
21. 27(4) at r3c6 : no 3,4,5 in r4c67
22. from step 7 : 11(3) : no 2,4 at r4c3 possible
23. from step 8 : 15(3) : no 7,9 at r6c7 possible -> 7,9 locked in r4c7 and r6c89 for N6
other way to put it: Killer pair {79} in r4c7 and r6c89 -> 7,9 locked for N6 (thanks Ed)
24. N6 : 14(2) = {68} -> 6,8 locked for r5 and N6
25. no 4 in r5c12, no 1 in r5c7
26. 7,9 locked in r134c7 for c7 -> no 2 in r28c7
27. from step 9 : 1 locked in 12(3) = 1{29|47} -> no 3
28. N9 : 16(3) : {259|457} blocked by 6(2)
29. N9 : 23(4) : {2579|4568 blocked by 6(2)
30. r6c12 : {49} not possible
30a. r6c12 = {49} -> r5c12 = {57}, r456c3 = {236} (from step 7), r4c12 = {18}, r4c89 = {24}, r6c89 = {37} -> conflict, can't place r5c67 = {34}
31. N4 : 12(2) = {39} -> 3,9 locked for r5 and N4
32. r5 : 7(2) = {25} -> 2,5 locked for r5
33. no 6 in r4c12
34. from step 8 : no 2,5 in r6c7
35. from step 7 : 11(3) = 4{16|25} -> no 7 in 11(3), no 1 at r4c3
36. -> 4 locked in r56c3 for c3 and N4 -> no 5 in r28c3
37. 7 locked in r5c45 for r5, N5 and 17(4) -> no 2 at r7c5
38. 3 locked in r4c45 for r4, N5 and 17(4)
39. N5 : 17(4) = {1736} -> 1,3,6,7 locked for N5
40. r456c3 = [542], r13c3 = [17]
41. N4 : 9(2) = {18} -> 1,8 locked for r4 and N4
42. r4c67 = [97], r13c7 = [96], r35c6 = [52], r56c7 = [53]
43. r79c7 = {24} -> 2,4 locked for c7 and N9
44. N12 : 8(3) = {134} -> r12c4 = {34} -> 3,4 locked for c4 and N2
45. r4c45 = [63], r12c6 = [81], r28c7 = [81], r6c6 = 4, r7c67 = [72], r9c7 = 4
46. N2 : 13(2) = {67} -> 6,7 locked for c5 and N2
47. r5c45 = [71]
48. N78 : 22(3) = {589} -> 5 locked in r89c4 for c4 and N8
49. r6c45 = [85], r7c345 = [914], r9c3 = 8, r89c5 = [82], r3c45 = [29], r2c1 = 9, r5c12 = [39]
50. N1 : 11(3) = {236}
51. r2c23 = [26], r3c12 = [83], r4c12 = [18], r12c5 = [67], r8c3 = 3, r78c2 = [64], r1c12 = [45], r12c4 = [34], r6c12 = [67], r789c1 = [527], r9c2 = 1, r89c6 = [63], r78c8 = [87], r1c89 = [27], r4c89 = [42], r5c89 = [68], r23c8 = [31], r23c9 = [54], r6c89 = [91], r78c9 = [39], r9c89 = [56], r89c4 = [59]
Comments appreciated.
Peter
Assassin 38
Assassin 38
Last edited by Nasenbaer on Sat Feb 17, 2007 11:32 pm, edited 1 time in total.
Looks like we've both used contradiction moves Peter. Found this to be the only way to break open this very tricky puzzle.Ruud wrote:Two columns are key. Keep squeezing until it explodes.
My 'squeeze' move comes much earlier than Peter's. Please let me know if anything can be more accurate or clearer.
First, one column
1. "45"n3 -> r13c7 = 15 = h15(2) = {69/78}
2. 6(2)n6 = {15/24}
3. 14(2)n6 = {59/68}
4. "45" n6 -> r456c7 = 15 = h15(3) = {159/249/357} (no 6, 8) = [2/5,4/5,5/9..]
4a. {168} blocked by h15(2)step 1
4b. {258} blocked by 14(2)n6
4c. {267} blocked by h15(2)step 1
4d. {348} -> 14(2)n6 = {59} but clashes with 6(2)n6
4e. {456} blocked by 6(2)n6
4f. no 1 r5c6
5.from h15(3)n6(step 4)-> 14(2)n6 {59} blocked = {68} only: locked for n6, r5
6. 10(2)n6 = {19/37} (no 2, 4) [edit: thanks Andrew]
7. "45" n9 -> r79c7 = 6 = h6(2) = {15/24} = [2/5,4/5..]
8. Killer pairs {25} and {45} in h6(2)n9 and h15(3)n6: (steps 4,7)
8a. 2,4,5 locked for c7
9. "45" c89 -> r28c7 = 9 = h9(2) = {18/36} (no 7.9)
10. 7(2)r5 = {25/34} (no 1) = [3/5..]
11. 12(2)n4 = {39/57} (no 4) = [3/5..]
12. -> Killer pair {35}: locked for r5
Now the second column
13. "45" n7 -> r79c3 = 17 = h17(2) = {89}:locked for n7, c3
14. "45" n4 -> r456c3 = 11 = h11(3) = {146/236/245} (no 7) = [2/6..] ({137} blocked by 12(2)n4)
15."45"n1 -> r13c3 = 8 = h8(2) = [17/]/{35} ([26] blocked by h11(3)n4)
15a. r1c3 = {135}, r3c3 = {357}
16. 1 locked in h8(2) or h11(3), r13456 for c3 (steps 14, 15)
17. "45"c12 -> r28c3 = 9 = h9(2)c3 = {27/36/45}
Now the squeeze
18. "45" r5 -> r5c345 = 12 = h12(3) = {129/147} = [7/9..] with [7/9] only in n5 in 17(4)
18a.can't have both 7 and 9 in a 17(4) (since 7+9=16) -> no 7,8 or 9 r4c45
19. don't know what happened to this one.
20. "45" r5 -> r5c3 + 5 = r4c45
21. Putting steps 18 and 20 together
1.r5c3 -> {r5c45}(step 18)
2.r5c3 + 5 -> {r4c45}(step 20)
21a.
1.r5c3 = 1 -> r5c45 = {29}
2.r5c3:1 + 5 = 6 -> r4c45 = {15} ({24} blocked by 21a.1)
21b.
1.r5c3 = 1 -> r5c45 = {47}
2.r5c3:1 + 5 = 6 -> r4c45 = {15} ({24} blocked by 21b.1)
21c.
1.r5c3 = 2 -> r5c45 = {19}
2.r5c3:2 + 5 = 7 -> r4c45 = Blocked:
..............................{16} blocked by 21c.1
..............................{25} blocked by 6(2)r4
..............................{34} -> 9(2)n4 = {18} only (remembering 2 in r5c3), but {14} in r4c1245 clashes with 6(2)n6.
21d.
1.r5c3 = 4 -> r5c45 = {17}
2.r5c3:4 + 5 = 9 -> r4c45 = {36} only
..................................{18/27} blocked by 21d.1
..................................{45} blocked by 6(2)r4
22. In summary:
22a. r5c3 = {14}
22b. r4c45 = {15/36} (no 2,4)
22c. 17(4)n5 = {1259/1457/1367} = 1{259/367/457}: 1 locked for n5
22d. no 8 r7c5
23. (step 14) h11(3)n4 = {146/245} (no 3) ({236} blocked by r5c3)
23a. = 4{16/25}: 4 locked for n4, c3
24. 13(2)n4 = {58/67} (no 9)
25. 9 n4 only in 12(2) = {39}:locked n4, r5
26. 7(2)r5 = {25}:locked r5
27. 7 for r5 only in n5: locked for n5
27a. no 2 r7c5
28. 9(2)n4 = {18/27} (no 5,6) = [1/2..]
28a. Killer pair {12} with 6(2)n6: locked for r4
29. 17(4)n5 = 17{36/45}: 1 locked for r5
29a. r5c3 = 4
30. r5c45 = {17} -> r4c45 = {36} locked for r4,n5
30a. no 3,6 r7c5
31. r4c3 = 5 -> r6c3 = 2 (h11(3))
32. 6(2) n6 = {24}:locked r4,n6
33. 7(2) r5 = [25]
34. 9(2)n4 = {18}:locked n4,r4
35. r4c67 = [97]
36. r6c7 = 3 (h15(3))
37. r13c7 = [96] (h15(2))
38. r13c3 = [17] (h8(2))
39. 9 n1 in c1: 9 locked c1 -> r5c12 = [39]
40. r3c6 = 5, r12c4 = {34}:locked n2,c4
40a. r4c45 = [63]
41. r12c6 = [81]
42. r28c7 = [81] (h9(2))
43. r12c5 = {67}:locked c5
the rest goes on
Last edited by sudokuEd on Wed Apr 04, 2007 1:11 am, edited 2 times in total.
Re: Assassin 38
Hmmm... if you say so. I finished this one already but still working on the album killer. Probably missing something obvious.Nasenbaer wrote:A really tough nut, Ruud. IMHO it was harder than your album killer. But after I realized what the key was it got easier. So here is the walkthrough, as always in tiny font.
-
rcbroughton
- Expert
- Posts: 143
- Joined: Wed Nov 15, 2006 1:45 pm
- Location: London
I'm with you Para, I didn't see anything particularly tricky in this one.
After the obvious 45 rule moves, it fell fairly quickly to cage combinations.
It was really thecage combinations in r4r5 r6 and n4 n6 that did it for me.
Here's a complete run-through of the order I did it.
[Edit] - tried to recreate this and realised I made an error at step 9 - couldn't see how I'd managed to get that elimination (although it was correct!!) I've gone through it again this evening, and had to solve around it a different way.
[Edit]Thanks to Andrew for some constructive comments on this one
1. 45 on n1: r13c3=8=[17]/[26]/{35}
Remember this one for later on - thanks Andrew
2. 45 on n3: r13c7=15={69}/{78}
... and remember this one for later on
3. 45 on n7: r79c3=17={89} locked for n7 and c3
4. 45 on n9: r79c7=6={15}/{24}
5. 45 on c12 r28c3=9={27}/{36}/{45} - no 1
6. 45 on c89 r28c7=9={18}/{27}/{36}/{45} - no 9
Missed an extra elimination here
6a. No {45} in r28c7 because it would clash with r79c7 from step 4 - thanks Andrew
7. 9(2)n4 - no 4,5 because of conflict with 6(2)n6
8. 9(2), 12(2) and 13(2) in n4 must use 79 - nowhere else in n4
8a. 12(2)n4 can only be {39}/{75} - {48} would force 9(2)={72} or {63} leaving no possible for 13(2)
Andrew comments I should have seen that this also eliminates {36} from 9(2) - I didn't find that until step 17
9b. 14(2)n6 {59} blocked by 12(2)n4 from 8a - can only be {68} locked for n6 - 10(2)n6={19}/{37}
9. 14(2) and 7(2) in r5 must use 35 - nowhere else in r5
9a. 7(2)n56 can only be {25}/{34}
I've reversed steps here, as it is more logical
10. 45 on r123 - r45c3+r4c67=25
10a. max r4c67=17, min r45c3=8, r45c3=[54]/[62]/[64]
10b. r45c3=8,9,10 -> r4c67=17,16,15
10c. r4c67=17 -> [89]
10d. r4c67=16 -> {79}
10e. r4c67=15 -> [87]
10f. r4c3={56}, r5c3={24}, r4c6={789}, r4c7={79}
11 killer pair {79} in n6 - r4c7 & 10(2) - no 7,9 in r6c7
12. 27(4)n2356 no 6,7,8,9 in r3c6
13. 45 n4 r456c3=11 =[641]/[623]/5{42} - no 5,6 in r6c3
14. must use 1 in 8(3)n12 - no 1 in r1c6
15. must use 9 in 22(3)n78 - no 9 in r9c56, no 1 in r8c5
16. 45 on r5 r5c345=12=2{19}/4{17}
16a. 1 locked in 17(4)n5, r5
16b. 17(4)n5 no 1,7,8,9 r4
16c. 9(2)n58 no 8 in r7c5
No longer need this step
17. 45 on r4 r4c34567=30 - must use 6 - no 6 in 9(2)n4 and no 3
18. 3 locked in 17(4)n5 for r4
18a 17(4)n5={1349}/{1367}
18b. 9(2)n58 - no 6 in r7c5
18c. 7(2)n56 - no 4 in r5c7
19. 9 locked in 27(4)n2356 for r4
19a. from 2, no 6 in r1c7
Major rework on this step after some pointers from Andrew
20. 45 rule n2. r1345c3+r4c6+r134c7=48
Remembering that from step 1 r13c3 total 8 and from step 2 r13c7 total 15
i) Possibilities for r13c3=8=[17]/[26]/{35}
ii) Possibilities for r13c7=15={78}/[96]
iii) so Possibilities for r134c7+r4c6 are...
20a. [9678]=30 - r1345c3=18 - r45c3=10 - r1345c3=[1764]/{35}[64]
20b. [9679]=31 - r1345c3=17 - r45c3=9 - r1345c3=[1754]/[2654]
20c. [7897]=31 - r1345c3=17 - r45c3=9 - r1345c3=[1754]/[2654]
20d. [8798]=32 - r1345c3=16 - r45c3=8 - r1345c3={35}[62] - but this would remove 8&2 from 9(2)n4 so not possible
20e. therefore r5c3=4
21 13(2)n4={58}/{76}
22 7(2)n56={25} - locked for r5
22a 12(2)n4={39} - locked for n4 and r5
23 17(4)n5={3617} - locked for n5
24 4 locked in 6(2)n6 for r4 ={42} locked for n6
24a 7(2)n56=[25]
25 1 locked in 9(2)n4 for r4 = {18} locked for n4, r4
25a 13(2)n4={67} locked for n4,r6
25b r4c3=5
25c 10(2)n6={19} locked for n6,r6
25d. r6c7=3
25e r4c7=7
25f r4c6=9
26 Naked single 2 at r6c3
27 hidden single 1 at r1c3 for c3
28 27(4)n2356 = [5697]/[3897]
29 killer pair {35} in n2 8(3) & r3c6
29a 13(2)={49}/{67}
29b. 18(3)=8{64}/[918]
30 9(2)n58={45}/[81]
31 45 on c5 r345c5=13=[931]
31a 17(4)n5=[6371]
31b. 13(2)n2={67} locked for n2, c5
31c. 9(2)n58={45} locked for c5
31d 10(2)n8={28} locked for n8
31e. 18(3)n23=[891]
32. 27(5)n124=[72954]
33 22(3)n78=8{59} - {59} locked for n8, c6
33a 10(2)n8=[82]
33b. 8(3)n12=1{34} - {34} locked for n2,c4
33c. 20(4)n4578 = [2891]
33d 27(4)n2356=[5697]
33e 16(4)n5689 = [4372]
33f 9(2)n58=[54]
34 13(3)n89={36}4
34a r8c7=1, r2c7=8
35 naked {36} at r8c36 for r8
36 12(3)n3=[831]
36a 10(2)n6=[91]
36b r3c9=4
36c 6(2)n6=[42]
36d 8(3)n12=[134]
36e r2c3=6, r8c3=3, r8c6=6, r9c6=3
37. 11(2)n1=[263]
37a r3c1=8
37b 9(2)n4=[18]
37c 12(2)n4=[39]
38 {45} locked in r1 of 26(4) n1
38a r2c1=9
38b 18(4)n3=[2754]
38c 13(2)n2=[67]
38d r8c9=9, r9c9=6
38e 14(2)n6=[68]
38f 23(4)n9=[3965]
38g 22(3)n78=[598]
38h 16(3)n9=[817]
38i 13(3)n7=[643]
38j 15(4)n7=[5271]
38k 26(4)n1=[4598]
38l 13(2)n4=[67]
Rgds
Richard
After the obvious 45 rule moves, it fell fairly quickly to cage combinations.
It was really thecage combinations in r4r5 r6 and n4 n6 that did it for me.
Here's a complete run-through of the order I did it.
[Edit] - tried to recreate this and realised I made an error at step 9 - couldn't see how I'd managed to get that elimination (although it was correct!!) I've gone through it again this evening, and had to solve around it a different way.
[Edit]Thanks to Andrew for some constructive comments on this one
1. 45 on n1: r13c3=8=[17]/[26]/{35}
Remember this one for later on - thanks Andrew
2. 45 on n3: r13c7=15={69}/{78}
... and remember this one for later on
3. 45 on n7: r79c3=17={89} locked for n7 and c3
4. 45 on n9: r79c7=6={15}/{24}
5. 45 on c12 r28c3=9={27}/{36}/{45} - no 1
6. 45 on c89 r28c7=9={18}/{27}/{36}/{45} - no 9
Missed an extra elimination here
6a. No {45} in r28c7 because it would clash with r79c7 from step 4 - thanks Andrew
7. 9(2)n4 - no 4,5 because of conflict with 6(2)n6
8. 9(2), 12(2) and 13(2) in n4 must use 79 - nowhere else in n4
8a. 12(2)n4 can only be {39}/{75} - {48} would force 9(2)={72} or {63} leaving no possible for 13(2)
Andrew comments I should have seen that this also eliminates {36} from 9(2) - I didn't find that until step 17
9b. 14(2)n6 {59} blocked by 12(2)n4 from 8a - can only be {68} locked for n6 - 10(2)n6={19}/{37}
9. 14(2) and 7(2) in r5 must use 35 - nowhere else in r5
9a. 7(2)n56 can only be {25}/{34}
I've reversed steps here, as it is more logical
10. 45 on r123 - r45c3+r4c67=25
10a. max r4c67=17, min r45c3=8, r45c3=[54]/[62]/[64]
10b. r45c3=8,9,10 -> r4c67=17,16,15
10c. r4c67=17 -> [89]
10d. r4c67=16 -> {79}
10e. r4c67=15 -> [87]
10f. r4c3={56}, r5c3={24}, r4c6={789}, r4c7={79}
11 killer pair {79} in n6 - r4c7 & 10(2) - no 7,9 in r6c7
12. 27(4)n2356 no 6,7,8,9 in r3c6
13. 45 n4 r456c3=11 =[641]/[623]/5{42} - no 5,6 in r6c3
14. must use 1 in 8(3)n12 - no 1 in r1c6
15. must use 9 in 22(3)n78 - no 9 in r9c56, no 1 in r8c5
16. 45 on r5 r5c345=12=2{19}/4{17}
16a. 1 locked in 17(4)n5, r5
16b. 17(4)n5 no 1,7,8,9 r4
16c. 9(2)n58 no 8 in r7c5
No longer need this step
17. 45 on r4 r4c34567=30 - must use 6 - no 6 in 9(2)n4 and no 3
18. 3 locked in 17(4)n5 for r4
18a 17(4)n5={1349}/{1367}
18b. 9(2)n58 - no 6 in r7c5
18c. 7(2)n56 - no 4 in r5c7
19. 9 locked in 27(4)n2356 for r4
19a. from 2, no 6 in r1c7
Major rework on this step after some pointers from Andrew
20. 45 rule n2. r1345c3+r4c6+r134c7=48
Remembering that from step 1 r13c3 total 8 and from step 2 r13c7 total 15
i) Possibilities for r13c3=8=[17]/[26]/{35}
ii) Possibilities for r13c7=15={78}/[96]
iii) so Possibilities for r134c7+r4c6 are...
20a. [9678]=30 - r1345c3=18 - r45c3=10 - r1345c3=[1764]/{35}[64]
20b. [9679]=31 - r1345c3=17 - r45c3=9 - r1345c3=[1754]/[2654]
20c. [7897]=31 - r1345c3=17 - r45c3=9 - r1345c3=[1754]/[2654]
20d. [8798]=32 - r1345c3=16 - r45c3=8 - r1345c3={35}[62] - but this would remove 8&2 from 9(2)n4 so not possible
20e. therefore r5c3=4
21 13(2)n4={58}/{76}
22 7(2)n56={25} - locked for r5
22a 12(2)n4={39} - locked for n4 and r5
23 17(4)n5={3617} - locked for n5
24 4 locked in 6(2)n6 for r4 ={42} locked for n6
24a 7(2)n56=[25]
25 1 locked in 9(2)n4 for r4 = {18} locked for n4, r4
25a 13(2)n4={67} locked for n4,r6
25b r4c3=5
25c 10(2)n6={19} locked for n6,r6
25d. r6c7=3
25e r4c7=7
25f r4c6=9
26 Naked single 2 at r6c3
27 hidden single 1 at r1c3 for c3
28 27(4)n2356 = [5697]/[3897]
29 killer pair {35} in n2 8(3) & r3c6
29a 13(2)={49}/{67}
29b. 18(3)=8{64}/[918]
30 9(2)n58={45}/[81]
31 45 on c5 r345c5=13=[931]
31a 17(4)n5=[6371]
31b. 13(2)n2={67} locked for n2, c5
31c. 9(2)n58={45} locked for c5
31d 10(2)n8={28} locked for n8
31e. 18(3)n23=[891]
32. 27(5)n124=[72954]
33 22(3)n78=8{59} - {59} locked for n8, c6
33a 10(2)n8=[82]
33b. 8(3)n12=1{34} - {34} locked for n2,c4
33c. 20(4)n4578 = [2891]
33d 27(4)n2356=[5697]
33e 16(4)n5689 = [4372]
33f 9(2)n58=[54]
34 13(3)n89={36}4
34a r8c7=1, r2c7=8
35 naked {36} at r8c36 for r8
36 12(3)n3=[831]
36a 10(2)n6=[91]
36b r3c9=4
36c 6(2)n6=[42]
36d 8(3)n12=[134]
36e r2c3=6, r8c3=3, r8c6=6, r9c6=3
37. 11(2)n1=[263]
37a r3c1=8
37b 9(2)n4=[18]
37c 12(2)n4=[39]
38 {45} locked in r1 of 26(4) n1
38a r2c1=9
38b 18(4)n3=[2754]
38c 13(2)n2=[67]
38d r8c9=9, r9c9=6
38e 14(2)n6=[68]
38f 23(4)n9=[3965]
38g 22(3)n78=[598]
38h 16(3)n9=[817]
38i 13(3)n7=[643]
38j 15(4)n7=[5271]
38k 26(4)n1=[4598]
38l 13(2)n4=[67]
Rgds
Richard
Last edited by rcbroughton on Wed Apr 18, 2007 6:36 pm, edited 1 time in total.
Another one that I only did fairly recently. It does have one contradiction move but a much simpler one than in the first two walkthroughs for this puzzle.
Richard's walkthrough did some excellent combination work that avoided the need for any contradiction moves. He always seems to get more out of large groups of innies or outies than the rest of us. I was particularly impressed by step 20 which broke the puzzle open.
Here is my walkthrough. There were times when I was struggling to find the way forward](./images/smilies/eusa_wall.gif "Brick wall")
so a few steps are just statements of combinations that I found while searching for useful steps. I've left them in because they show what I was looking at. Then I found the eliminations in N6 (step 28) and the key 45 in R5 (step 32). After that a short contradiction move in step 33 breaks it open.
Clean-up is used in various steps, using the combinations in steps 1 to 10 for further eliminations from these two cell cages and for split cages formed by the use of the 45 rule.
Thanks Ed for pointing out the flaw in step 28b.
1. R12C5 = {49/58/67}, no 1,2,3
2. R4C12 = {18/27/36/45}, no 9
3. R4C89 = {15/24}
4. R5C12 = {39/48/57}, no 1,2,6
5. R5C67 = {16/25/34}, no 7,8,9
6. R5C89 = {59/68}
7. R6C12 = {49/58/67}, no 1,2,3
8. R67C5 = {18/27/36/45}, no 9
9. R6C89 = {19/28/37/46}, no 5
10. R89C5 = {19/28/37/46}, no 5
11. 8(3) cage in N12 = 1{25/34}, no 1 in R1C6
12. 11(3) cage in N1 = {128/137/146/236/245}, no 9
13. 22(3) cage in N78 = 9{58/67}, no 9 in R9C56, clean-up: no 1 in R8C5
14. 26(4) cage in N1 = {2789/3689/4589/4679/5678}, no 1
15. 27(4) cage in N2356 = 9{378/468/567}, no 1,2
16. 45 rule on N1 2 innies R13C3 = 8 = [17/26/35/53]
17. 9 in N1 locked in 26(4) cage = 9{278/368/458/467}
18. 45 rule on N3 2 innies R13C7 = 15 = {69/78}
19. 45 rule on N7 2 innies R79C3 = 17 = {89}, locked for C3 and N7
20. 45 rule on N9 2 innies R79C7 = 6 = {15/24}
21. 45 rule on C12 2 outies R28C3 = 9 = {27/36/45}, no 1
22. 45 rule on C89 2 outies R28C7 = 9 = {18/27/36} (cannot be {45} which would clash with R79C7), no 4,5,9
23. 13(3) cage in N7 = {157/247/256/346}
24. 15(4) cage in N7 = {1257/1347/1356/2346}
25. 45 rule on N4 3 innies R456C3 = 11 = {146/236/245} (cannot be {137} which clashes with all possible combinations for R56C12), no 7
25a. R456C3 must contain 1 or 2 -> R4C12 must contain 1 or 2 = {18/27}, no 3,4,5,6
[Edit. Step number corrected.]
25b. If R4C12 = {18} => R5C12 cannot be {48}
If R4C12 = {27} => R456C3 => {146} => R5C12 cannot be {48}
-> no 4,8 in R5C12
[Edit. Step 25b added for use with the corrected step 28b. Thanks Richard for giving me the idea for step 25b which I hadn’t spotted before I saw your walkthrough.]
26. Killer pair 1/2 in R4C12 and R4C89 for R4
27. 9 in C2 locked in R156C2
27a. 45 rule on C1 5 outies R14569C2 = 30 = 9{1578/2478/2568/3468/3567}, must contain two of 6,7,8
27b. 45 rule on C2 4 innies R2378C2 = 15 = {1248/1257/1347/1356/2346}
28. 45 rule on N6 3 innies R456C7 = 15 = {159/168/249/357} (cannot be {258/456} which clash with R5C89, cannot be {267/348} which clash with the combination of R45C89)
28a. For the valid combinations for R456C7, after working the interactions with the other three cages in N6, R6C89 can only be {19/37}, no 2,4,6,8
[Edit. An alternative way, suggested by Ed, that eliminates 2,4,6,8 from R6C89.]
If R4C89 = {24} => no 2,4,6,8 in R6C89
If R4C89 = {15} => R5C89 = {68} => no 2,4,6,8 in R6C89
-> R6C89 = {19/37}
The original step 28b was flawed. Thanks Ed for pointing that out. Here is a replacement step.
28b. R5C12 = {39/57} -> R5C89 = {68} (cannot be {59} which clashes with R5C12)
28c. R5C89 = {68} (hidden pair in N6), locked for R5, clean-up: no 1 in R5C67
[Edit. Clean-up edited after adding step 25b and changing step 28b.]
28d. Killer pair 3/5 in R5C12 and R5C67 for R5
28e. 45 rule on R5 3 innies R5C345 = 12 = 1{29/47}
28f. R456C7 = {159/249/357} [1/2/3, 4/5, 7/9]
29. Killer pair 7/9 in R13C7 and R456C7 for C7, clean-up: no 2 in R28C7
30. 45 rule on R4 5 innies R4C34567 = 30 and must contain 3,6,9 = 369{48/57}
31. 45 rule on R6 5 innies R6C34567 = 22 and must contain 2 = 2{1469/1568/3458/3467} (cannot be 2{1379/1478} which clash with R6C89)
32. 45 rule on R5 2 outies R4C45 – 5 = 1 innie R5C3, min R4C45 = 7 -> min R5C3 = 2, max R5C3 = 4 -> max R4C45 = 9, no 7,8,9
32a. R5C345 = 1{29/47}, R5C3 = {24}, no 2,4 in R5C45
32b. 1 in R5 locked in R5C45, locked for N5, clean-up: no 8 in R7C5
33. If R5C3 = 2, R5C67 = {34}, R4C45 = 7 (step 32) = {34} -> R5C3 <>2
33a. R5C3 = 4, clean-up: no 5 in R28C3, no 3 in R5C67 = {25}, locked for R5, R5C45 = {17} (step 28e), locked for R5 and N5, R5C12 = {39}, locked for N4, R4C45 = 9 = {36} (cannot be {45} which would clash with R4C89), locked for R4 and N5, clean-up: no 2,3,6 in R7C5
34. R4C3 = 5 (naked single), clean-up: no 3 in R13C3, no 1 in R4C89 = {24}, locked for R4 and N6, no 8 in R6C12 = {67}, locked for R6 and N4, no 3 in R6C89 = {19}, locked for R6 and N6
35. R5C67 = [25], R4C7 = 7, R6C3 = 2, R6C7 = 3, R1C3 = 1 (naked singles), clean-up: R3C3 = 7, no 7 in R7C5, no 8 in R13C7 = {69}, locked for C7 and N3, no 1 in R79C7 = {24}, locked for N9
36. R6C456 = {458}, locked for N5
37. R4C6 = 9, R3C7 = 6, R1C7 = 9 (naked singles), R3C6 = 5 (cage sum), clean-up: no 2 in R12C4, no 8 in R12C5, no 4 in R2C5
38. R12C4 = {34}, locked for C4 and N2, clean-up: no 9 in R2C5
38a. R12C5 = {67}, locked for C5 and N2, clean-up: no 3,4 in R89C5
39. R4C45 = [63], R5C45 = [71], R12C6 = [81], R28C7 = [81], R6C6 = 4, R79C7 = [24] (naked singles), R7C6 = 7 (cage sum), clean-up: no 9 in R8C5
40. R3C4 = 2 (hidden single in C4) -> R3C5 = 9
41. 22(3) cage in N78 = {589} -> no 8 in R9C5, R89C5 = [82], R89C4 = {59}, locked for C4, N8 and 22(3) cage
42. R6C45 = [85], R7C45 = [14], R79C3 = [98] (naked singles)
43. R2C1 = 9 (hidden single in N1) -> R5C12 = [39]
44. R2C7 = 8 -> R23C8 = 4 = [31] (only remaining combination)
and the rest is naked singles
Richard's walkthrough did some excellent combination work that avoided the need for any contradiction moves. He always seems to get more out of large groups of innies or outies than the rest of us. I was particularly impressed by step 20 which broke the puzzle open.
Here is my walkthrough. There were times when I was struggling to find the way forward
so a few steps are just statements of combinations that I found while searching for useful steps. I've left them in because they show what I was looking at. Then I found the eliminations in N6 (step 28) and the key 45 in R5 (step 32). After that a short contradiction move in step 33 breaks it open.Clean-up is used in various steps, using the combinations in steps 1 to 10 for further eliminations from these two cell cages and for split cages formed by the use of the 45 rule.
Thanks Ed for pointing out the flaw in step 28b.
1. R12C5 = {49/58/67}, no 1,2,3
2. R4C12 = {18/27/36/45}, no 9
3. R4C89 = {15/24}
4. R5C12 = {39/48/57}, no 1,2,6
5. R5C67 = {16/25/34}, no 7,8,9
6. R5C89 = {59/68}
7. R6C12 = {49/58/67}, no 1,2,3
8. R67C5 = {18/27/36/45}, no 9
9. R6C89 = {19/28/37/46}, no 5
10. R89C5 = {19/28/37/46}, no 5
11. 8(3) cage in N12 = 1{25/34}, no 1 in R1C6
12. 11(3) cage in N1 = {128/137/146/236/245}, no 9
13. 22(3) cage in N78 = 9{58/67}, no 9 in R9C56, clean-up: no 1 in R8C5
14. 26(4) cage in N1 = {2789/3689/4589/4679/5678}, no 1
15. 27(4) cage in N2356 = 9{378/468/567}, no 1,2
16. 45 rule on N1 2 innies R13C3 = 8 = [17/26/35/53]
17. 9 in N1 locked in 26(4) cage = 9{278/368/458/467}
18. 45 rule on N3 2 innies R13C7 = 15 = {69/78}
19. 45 rule on N7 2 innies R79C3 = 17 = {89}, locked for C3 and N7
20. 45 rule on N9 2 innies R79C7 = 6 = {15/24}
21. 45 rule on C12 2 outies R28C3 = 9 = {27/36/45}, no 1
22. 45 rule on C89 2 outies R28C7 = 9 = {18/27/36} (cannot be {45} which would clash with R79C7), no 4,5,9
23. 13(3) cage in N7 = {157/247/256/346}
24. 15(4) cage in N7 = {1257/1347/1356/2346}
25. 45 rule on N4 3 innies R456C3 = 11 = {146/236/245} (cannot be {137} which clashes with all possible combinations for R56C12), no 7
25a. R456C3 must contain 1 or 2 -> R4C12 must contain 1 or 2 = {18/27}, no 3,4,5,6
[Edit. Step number corrected.]
25b. If R4C12 = {18} => R5C12 cannot be {48}
If R4C12 = {27} => R456C3 => {146} => R5C12 cannot be {48}
-> no 4,8 in R5C12
[Edit. Step 25b added for use with the corrected step 28b. Thanks Richard for giving me the idea for step 25b which I hadn’t spotted before I saw your walkthrough.]
26. Killer pair 1/2 in R4C12 and R4C89 for R4
27. 9 in C2 locked in R156C2
27a. 45 rule on C1 5 outies R14569C2 = 30 = 9{1578/2478/2568/3468/3567}, must contain two of 6,7,8
27b. 45 rule on C2 4 innies R2378C2 = 15 = {1248/1257/1347/1356/2346}
28. 45 rule on N6 3 innies R456C7 = 15 = {159/168/249/357} (cannot be {258/456} which clash with R5C89, cannot be {267/348} which clash with the combination of R45C89)
28a. For the valid combinations for R456C7, after working the interactions with the other three cages in N6, R6C89 can only be {19/37}, no 2,4,6,8
[Edit. An alternative way, suggested by Ed, that eliminates 2,4,6,8 from R6C89.]
If R4C89 = {24} => no 2,4,6,8 in R6C89
If R4C89 = {15} => R5C89 = {68} => no 2,4,6,8 in R6C89
-> R6C89 = {19/37}
The original step 28b was flawed. Thanks Ed for pointing that out. Here is a replacement step.
28b. R5C12 = {39/57} -> R5C89 = {68} (cannot be {59} which clashes with R5C12)
28c. R5C89 = {68} (hidden pair in N6), locked for R5, clean-up: no 1 in R5C67
[Edit. Clean-up edited after adding step 25b and changing step 28b.]
28d. Killer pair 3/5 in R5C12 and R5C67 for R5
28e. 45 rule on R5 3 innies R5C345 = 12 = 1{29/47}
28f. R456C7 = {159/249/357} [1/2/3, 4/5, 7/9]
29. Killer pair 7/9 in R13C7 and R456C7 for C7, clean-up: no 2 in R28C7
30. 45 rule on R4 5 innies R4C34567 = 30 and must contain 3,6,9 = 369{48/57}
31. 45 rule on R6 5 innies R6C34567 = 22 and must contain 2 = 2{1469/1568/3458/3467} (cannot be 2{1379/1478} which clash with R6C89)
32. 45 rule on R5 2 outies R4C45 – 5 = 1 innie R5C3, min R4C45 = 7 -> min R5C3 = 2, max R5C3 = 4 -> max R4C45 = 9, no 7,8,9
32a. R5C345 = 1{29/47}, R5C3 = {24}, no 2,4 in R5C45
32b. 1 in R5 locked in R5C45, locked for N5, clean-up: no 8 in R7C5
33. If R5C3 = 2, R5C67 = {34}, R4C45 = 7 (step 32) = {34} -> R5C3 <>2
33a. R5C3 = 4, clean-up: no 5 in R28C3, no 3 in R5C67 = {25}, locked for R5, R5C45 = {17} (step 28e), locked for R5 and N5, R5C12 = {39}, locked for N4, R4C45 = 9 = {36} (cannot be {45} which would clash with R4C89), locked for R4 and N5, clean-up: no 2,3,6 in R7C5
34. R4C3 = 5 (naked single), clean-up: no 3 in R13C3, no 1 in R4C89 = {24}, locked for R4 and N6, no 8 in R6C12 = {67}, locked for R6 and N4, no 3 in R6C89 = {19}, locked for R6 and N6
35. R5C67 = [25], R4C7 = 7, R6C3 = 2, R6C7 = 3, R1C3 = 1 (naked singles), clean-up: R3C3 = 7, no 7 in R7C5, no 8 in R13C7 = {69}, locked for C7 and N3, no 1 in R79C7 = {24}, locked for N9
36. R6C456 = {458}, locked for N5
37. R4C6 = 9, R3C7 = 6, R1C7 = 9 (naked singles), R3C6 = 5 (cage sum), clean-up: no 2 in R12C4, no 8 in R12C5, no 4 in R2C5
38. R12C4 = {34}, locked for C4 and N2, clean-up: no 9 in R2C5
38a. R12C5 = {67}, locked for C5 and N2, clean-up: no 3,4 in R89C5
39. R4C45 = [63], R5C45 = [71], R12C6 = [81], R28C7 = [81], R6C6 = 4, R79C7 = [24] (naked singles), R7C6 = 7 (cage sum), clean-up: no 9 in R8C5
40. R3C4 = 2 (hidden single in C4) -> R3C5 = 9
41. 22(3) cage in N78 = {589} -> no 8 in R9C5, R89C5 = [82], R89C4 = {59}, locked for C4, N8 and 22(3) cage
42. R6C45 = [85], R7C45 = [14], R79C3 = [98] (naked singles)
43. R2C1 = 9 (hidden single in N1) -> R5C12 = [39]
44. R2C7 = 8 -> R23C8 = 4 = [31] (only remaining combination)
and the rest is naked singles